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Let f:[0,2]vecR be a function which is c...

Let `f:[0,2]vecR` be a function which is continuous on [0,2] and is differentiable on (0,2) with `f(0)=1` `L e t :F(x)=int_0^(x^2)f(sqrt(t))dt` for `x` in `[0,2]`. If `F^(prime)(x)=f^(prime)(x)` . for all `x in (0,2),` then `F(2)` equals

A

`e^(2)-1`

B

`e^(4)-1`

C

`e-1`

D

`e^(4)`

Text Solution

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The correct Answer is:
B
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